Answer-first summary for fast verification
Answer: USD 5.86
The correct answer is USD 5.86, which is calculated using the binomial option pricing model with risk-neutral probabilities. **Key Calculation Steps:** 1. **Risk-neutral probability of up move**: 57.61% (given from previous question) 2. **Final node payoffs**: - Node [D]: max(0, 52-72) = 0 - Node [E]: max(0, 52-48) = 4 - Node [F]: max(0, 52-32) = 20 3. **Backward induction**: - **Node [B]**: (0.5761×0 + 0.4239×4) × exp(-0.12×3/12) = 1.65 (intrinsic value = 0, so no early exercise) - **Node [C]**: (0.5761×4 + 0.4239×20) × exp(-0.12×3/12) = 10.46 (intrinsic value = 12, so early exercise at 12) - **Node [A]**: (0.5761×1.65 + 0.4239×12) × exp(-0.12×3/12) = 5.86 (intrinsic value = 2, so no early exercise) **Why other options are incorrect:** - **A (USD 2.00)**: This is the intrinsic value at node A (max(0, 52-50) = 2), but doesn't account for time value - **B (USD 5.23)**: This would be the value if it were a European put option (exercisable only at expiration) - **D (USD 6.04)**: This value doesn't match the calculated no-arbitrage price using the binomial model
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
At Bank XYZ, a risk manager is evaluating the sale of a 6-month American-style put option on stock ABC, which does not pay dividends. The stock is currently trading at USD 50, and the option has a strike price of USD 52. To determine the no-arbitrage price of the option, the manager applies a two-step binomial tree model. In each step, the stock price may either rise or fall by 20%. The manager estimates an 80% probability of an upward movement and a 20% probability of a downward move in each period. The annual continuously compounded risk-free rate is 12%.
The no-arbitrage price of the option is closest to:
A
USD 2.00
B
USD 5.23
C
USD 5.86
D
USD 6.04
No comments yet.